Data Exploration Gabriel Hamulic

Dataset: US Real Estate Dataset

Instructions

Your report must be of high quality, meaning that your report:

• is visually and textually pleasing of
• does not look/read/feel like a draft instead of a finished analysis
• explains/discusses your findings and results in the main text, e.g., explain/discuss all figures/table in the main text
• is representable such that it can show to any interested third party
• uses figure/table captions/linking/reference (see example further down)
• Do not show any standard printout of R-code, use for data.frame/tibbles knitr::kable() printing.
• Do not simply print datasets (too many lines) use instead rmarkdown::paged_table()

Introduction

Libraries

library <- function(...) {suppressPackageStartupMessages(base::library(...))}
library(tidyverse)
library(dplyr)
library(knitr)
library(tidyr)
library(rmarkdown)
library(janitor)
library(scales)
library(tidytext)
library(ggforce)
library(GGally)
library(DT)
library(kableExtra)

Data

Data source

In this data exploration we are looking at the US Real Estate market with use of a dataset from kaggle published by Ahmed Shahriar Sakib. It contains over 2.2 Million Real Estate listings broken down to State, Size, Price (among other factors). (Source: https://www.kaggle.com/datasets/ahmedshahriarsakib/usa-real-estate-dataset/data)

Data import

data = read.csv("data/realtor-data.zip.csv") # Data import

Data Transformation

data = subset(data, select = c(status, price, bed, bath, acre_lot, city, state, house_size)) # keep relevant columns

Structure with standard datatypes

str_out <- capture.output(str(data))
kable(data.frame(Output = str_out), col.names = "Structure Output")

Structure Output
‘data.frame’: 2226382 obs. of 8 variables:
$ status : chr “for_sale” “for_sale” “for_sale” “for_sale” …
$ price : num 105000 80000 67000 145000 65000 179000 50000 71600 100000 300000 …
$ bed : int 3 4 2 4 6 4 3 3 2 5 …
$ bath : int 2 2 1 2 2 3 1 2 1 3 …
$ acre_lot : num 0.12 0.08 0.15 0.1 0.05 0.46 0.2 0.08 0.09 7.46 …
$ city : chr “Adjuntas” “Adjuntas” “Juana Diaz” “Ponce” …
$ state : chr “Puerto Rico” “Puerto Rico” “Puerto Rico” “Puerto Rico” …
$ house_size: num 920 1527 748 1800 NA …

# Assign Data Types
data$status = as.factor(data$status)
data$city = as.factor(data$city)
data$state = as.factor(data$state)

NA Removal

before_rows <- nrow(data)
data <- na.omit(data)
after_rows <- nrow(data)
kable(data.frame(Description = c("Before NA removal", "After NA removal"),
Rows = c(before_rows, after_rows)))

Description	Rows
Before NA removal	2226382
After NA removal	1360716

The dataset now has 1360716 observations and 8 variables after removing rows with missing values.

Filtering

# Filter min and max values
data = data |>
  filter(price > 10000 & price < 1000000000)

Calculations

data = data |>
  mutate(price_per_sqm = price/house_size)

Cleaned Dataset

paged_table(data)

Structure after transformation

str_out <- capture.output(str(data))
kable(data.frame(Output = str_out), col.names = "Structure Output")

Structure Output
‘data.frame’: 1360076 obs. of 9 variables:
$ status : Factor w/ 3 levels “for_sale”,“ready_to_build”,..: 1 1 1 1 1 1 1 1 1 1 …
$ price : num 105000 80000 67000 145000 179000 50000 71600 100000 300000 89000 …
$ bed : int 3 4 2 4 4 3 3 2 5 3 …
$ bath : int 2 2 1 2 3 1 2 1 3 2 …
$ acre_lot : num 0.12 0.08 0.15 0.1 0.46 …
$ city : Factor w/ 20099 levels ““,”100 89 Lower Shepard Creek Road”,..: 94 94 8790 14316 15873 3276 14316 14316 9696 8556 …
$ state : Factor w/ 56 levels ““,”Alabama”,“Alaska”,..: 43 43 43 43 43 43 43 43 43 43 …
$ house_size : num 920 1527 748 1800 2520 …
$ price_per_sqm: num 114.1 52.4 89.6 80.6 71 …
- attr(*, “na.action”)= ‘omit’ Named int [1:865666] 5 24 43 44 52 60 61 62 63 64 …
..- attr(*, “names”)= chr [1:865666] “5” “24” “43” “44” …

We chose the following data types for our variables:

Data dictionary

tibble(
  Variable = c("price", "status", "acre_lot", "state", "house_size"),
  Description = c(
    "The price for which the item was listed on the market",
    "The status if the house is already sold or still for sale",
    "The size of the land / lot on which the house is located in acres",
    "The state in which the house is located",
    "The size of the house in square feet"
  )
) |>
  kable(
    caption = "Description of key variables in the dataset",
    align = c("l", "l")
  )

Description of key variables in the dataset

Variable	Description
price	The price for which the item was listed on the market
status	The status if the house is already sold or still for sale
acre_lot	The size of the land / lot on which the house is located in acres
state	The state in which the house is located
house_size	The size of the house in square feet

Summary statistic tables

In this section we will cover the summary of our cleaned dataset. We will explore basic statistical values from our data.

Numeric Statistics

Summary of numerical values

data |> 
  janitor::clean_names() |>
  mutate(row = row_number() |> factor()) |> 
  pivot_longer(cols = where(is.numeric)) |> 
  group_by(name) |> 
  summarize(N = n(),
            min = min(value),
            mean = mean(value),
            median = median(value),
            max = max(value),
            st.dev = sd(value)
            ) |> 
  knitr::kable(digits = 2)

Summary statistics of numerical variables in dataframe

name	N	min	mean	median	max	st.dev
acre_lot	1360076	0.00	12.75	0.21	100000.0	799.83
bath	1360076	1.00	2.54	2.00	222.0	1.36
bed	1360076	1.00	3.39	3.00	444.0	1.43
house_size	1360076	100.00	2119.39	1812.00	1560780.0	4069.66
price	1360076	10400.00	573730.62	379000.00	515000000.0	1226596.98
price_per_sqm	1360076	0.02	262.42	197.42	491412.2	500.86

Visualisation of numerical values

data |>
  clean_names() |>
  pivot_longer(cols = where(is.numeric)) |>
  ggplot(aes(x = value, fill = name)) +
  geom_histogram(bins = 30, alpha = 0.7, color = "white") +
  scale_x_log10(labels = label_comma()) +   # 👈 echte Werte, log-Skala
  facet_wrap(~ name, scales = "free_x") +
  theme_minimal() +
  labs(
    title = "Distribution of Numerical Variables (logarithmic scale)",
    x = "Value",
    y = "Count"
  ) +
  theme(
    legend.position = "none",
    axis.text.x = element_text(angle = 25, hjust = 1) 
    )

Nominal Statistics

Summary of nominal variables (top categories)

top_n_per_var <- 10 

nominal_summary <- data |>
  clean_names() |>
  select(where(is.factor), price) |>
  pivot_longer(cols = where(is.factor),
               names_to = "Variable",
               values_to = "Category") |>
  group_by(Variable, Category) |>
  summarise(
    Count = n(),
    Percent = round(100 * Count / nrow(data), 2),
    Mean_Price = round(mean(price, na.rm = TRUE), 0),
    .groups = "drop"
  ) |>
  group_by(Variable) |>
  slice_max(order_by = Count, n = top_n_per_var, with_ties = FALSE) |>
  ungroup()

kable(
  nominal_summary,
  caption = paste0(
    "Top ", top_n_per_var,
    " categories per factor variable (counts, share %, and mean price)"
  ),
  digits = 2,
  align = c("l", "l", "r", "r", "r")
)

Top categories for factor variables with counts, proportions, and mean price

Variable	Category	Count	Percent	Mean_Price
city	Houston	19226	1.41	477651
city	Tucson	7876	0.58	384816
city	Phoenix	7694	0.57	543665
city	Los Angeles	7556	0.56	1885626
city	Dallas	7510	0.55	587276
city	Philadelphia	7336	0.54	338467
city	Richmond	6592	0.48	392538
city	Orlando	6281	0.46	418841
city	Fort Worth	6171	0.45	389780
city	Saint Louis	5970	0.44	250029
state	California	170954	12.57	1095518
state	Texas	145394	10.69	451253
state	Florida	127675	9.39	649826
state	Arizona	54488	4.01	552916
state	Pennsylvania	51922	3.82	343792
state	New York	50935	3.75	669257
state	Georgia	49234	3.62	422988
state	Illinois	46901	3.45	357316
state	Washington	46450	3.42	728113
state	Virginia	44236	3.25	547994
status	for_sale	750493	55.18	621383
status	sold	609583	44.82	515063

Visualisation of nominal variables (top categories)

nominal_summary <- nominal_summary |>
  group_by(Variable) |>
  mutate(Category = forcats::fct_reorder(Category, Count),
         Category = factor(Category, levels = unique(Category))) |>
  ungroup()

# Plot: Facets untereinander, mit eigener x-Skala und y-Skala pro Variable
ggplot(nominal_summary, aes(x = Count, y = Category, fill = Variable)) +
  geom_col(show.legend = FALSE, alpha = 0.8, width = 0.7) +
  facet_wrap(~ Variable, ncol = 1, scales = "free", drop = TRUE) +
  scale_x_continuous(labels = label_comma()) +   #Tausendertrennung, keine 1e+05
  theme_minimal() +
  labs(
    title = "Top Categories per Factor Variable",
    x = "Count",
    y = "Category"
  ) +
  theme(
    panel.spacing.y = unit(1, "lines"),
    strip.text = element_text(size = 12, face = "bold"),
    axis.text.y = element_text(size = 8),
    plot.margin = margin(5, 15, 5, 5)
  )

Bivariate Analysis

Pairs Plot (all numeric variables)

set.seed(123)

data_num <- data |>
  janitor::clean_names() |>
  select(where(is.numeric)) |>
  slice_sample(n = 3000) |>
  mutate(across(everything(), log1p)) 

p <- ggpairs(
  data_num,
  progress = FALSE,
  upper = list(continuous = wrap("cor", size = 4, alignPercent = 0.8, stars = TRUE)),
  lower = list(continuous = wrap("points", alpha = 0.3, size = 0.7)),
  diag = list(continuous = wrap("densityDiag", alpha = 0.7))
)

p +
  theme_minimal(base_size = 11) +
  theme(
    strip.text = element_text(size = 8, face = "bold"),
    panel.grid = element_blank(),
    axis.text = element_text(size = 8),
    axis.title = element_text(size = 9),
    plot.title = element_text(face = "bold", size = 14, hjust = 0.5)
  ) +
  labs(title = "Scatterplot-Matrix (log-transformiert, n=3000)")

Price vs. house size by listing status

library(dplyr)
library(plotly)

# Stichprobe ziehen für Performance
set.seed(123)
sample_data <- data %>% sample_n(50000)

plot_ly(
  sample_data,
  x = ~house_size,
  y = ~price,
  color = ~status,
  type = "scatter",
  mode = "markers",
  alpha = 0.6
) %>%
  plotly::layout(
    title = list(text = "Relationship Between House Size and Price by Status"),
    xaxis = list(title = "House Size (sqft)"),
    yaxis = list(title = "Price ($)", type = "log")
  )

Multiple Regression

model <- lm(price ~ house_size + bath + bed + state + status, data = data)
library(broom)
tidy(model) |>
  arrange(p.value) |>
  mutate(
    estimate = round(estimate, 1),
    std.error = round(std.error, 1),
    statistic = round(statistic, 1),
    p.value = signif(p.value, 3)
  ) |>
  datatable(
    caption = "Regressionsergebnisse (interaktiv)",
    filter = "top",         
    options = list(
      pageLength = 10,      
      autoWidth = TRUE,
      responsive = TRUE
    )
  )

tidy(model, conf.int = TRUE) |>
  filter(term != "(Intercept)") |>
  mutate(term = reorder(term, estimate)) |>
  ggplot(aes(x = estimate, y = term, fill = estimate > 0)) +
  geom_col(show.legend = FALSE) +
  geom_vline(xintercept = 0, linetype = "dashed") +
  theme_minimal() +
  labs(
    title = "Greatest contributors to price",
    x = "regression coefficient",
    y = ""
  )

USA Map – Average Price

library(dplyr)
library(tibble)

valid_states <- tibble(
  state_name = c(state.name, "District of Columbia"),
  state_abbr = c(state.abb,  "DC")
)

library(dplyr)
library(plotly)

map_price <- data |>
  group_by(state) %>%
  summarise(avg_price = mean(price, na.rm = TRUE), .groups = "drop") |>
  inner_join(valid_states, by = c("state" = "state_name")) |>
  mutate(avg_price_k = avg_price / 1000)

plot_ly(
  map_price,
  type = "choropleth",
  locationmode = "USA-states",
  locations = ~state_abbr,
  z = ~avg_price_k,
  text = ~paste0(state, "<br>Avg Price: $", round(avg_price_k, 1), "K"),
  colorscale = "Blues",
  colorbar = list(title = "Avg Price ($K)")
) |>
  plotly::layout(
    title = list(text = "Average Property Price by U.S. State"),
    geo = list(scope = "usa", projection = list(type = "albers usa"))
  )

USA Map AVG Size (Karte)

map_size <- data %>%
  group_by(state) %>%
  summarise(avg_size = mean(house_size, na.rm = TRUE), .groups = "drop") %>%
  inner_join(valid_states, by = c("state" = "state_name"))

plot_ly(
  map_size,
  type = "choropleth",
  locationmode = "USA-states",
  locations = ~state_abbr,
  z = ~avg_size,
  text = ~paste0(state, "<br>Avg Size: ", round(avg_size), " sqft"),
  colorscale = "Greens",
  colorbar = list(title = "Avg Size (sqft)")
) %>%
  plotly::layout(
    title = list(text = "Average House Size by U.S. State"),
    geo = list(scope = "usa", projection = list(type = "albers usa"))
  )

USA Map Extremfälle Price (Karte)

map_extremes <- data %>%
  group_by(state) %>%
  summarise(
    min_price = suppressWarnings(min(price, na.rm = TRUE)),
    max_price = suppressWarnings(max(price, na.rm = TRUE)),
    .groups = "drop"
  ) %>%
  mutate(range_price = max_price - min_price) %>%
  inner_join(valid_states, by = c("state" = "state_name"))

plot_ly(
  map_extremes,
  type = "choropleth",
  locationmode = "USA-states",
  locations = ~state_abbr,
  z = ~range_price,
  text = ~paste0(
    state,
    "<br>Min: $", formatC(min_price, big.mark = ",", format = "f", digits = 0),
    "<br>Max: $", formatC(max_price, big.mark = ",", format = "f", digits = 0)
  ),
  colorscale = "Reds",
  colorbar = list(title = "Price Range ($)")
) %>%
  plotly::layout(
    title = list(text = "Price Extrem Values by U.S. State (Max − Min)"),
    geo = list(scope = "usa", projection = list(type = "albers usa"))
  )

Anzahl aktiver Listings pro State

Summary

Instructions

Summarise your finding.